ON THE SEMANTICS OF OPTIONAL.
The semantics of OPTIONAL as specified in the document, if we assume
a relational-like algebra, should be more precisely defined as
follows:
QA OPTIONAL QB
is defined as:
(QA . QB) UNION (QA \setminus \project_{V-QA}(QA . QB))
where \project_{V-QA}(Q) is the projection of the solutions of Q over
the variables of QA.
We can show that it is possible to give a standard relational algebra
account of the whole SPARQL (excluding, of course, the GRAPH parts;
and leaving the minimisation routine and the CONSTRUCT outside the
algebra.).
OUR CONCLUSIONS
We are not proposing a different semantics for OPTIONAL, but just a
better version of it as an algebraic operator. The "parallel" optional
construct needs still to be formalised.